\(\mathsf {Tribes}_{m,n} = \mathsf {OR}_m \circ \mathsf {AND}_n\)  is a non-symmetric function, made by composing \(\mathsf {OR}\)  and \(\mathsf {AND}\) . We use it as an example of a total function where \(\mathsf {R}\)  and \(\mathsf {CG}^{\text{pub}}\)  are asymptotically different. It can be verified that \(\mathsf {Tribes}_{\sqrt{n},\sqrt{n}}) = \Theta (\sqrt{n})\) , and \(\lambda (\mathsf {Tribes}_{\sqrt{n},\sqrt{n}}) = \mathsf {Q}(\mathsf {Tribes}_{\sqrt{n},\sqrt{n}}) =\Theta (\sqrt{n})\)  follows from composition [1]}, [2]}. \(\mathsf {R}(\mathsf {Tribes}_{\sqrt{n},\sqrt{n}}) = \Theta (n)\)  is from Jain and Klauck [3]}, other measures follow from these observations.
